Outline of categorical semiotics
November 3, 2019 — Brad Venner
syntax, semantics, pragmatics
towards categorical pragmatics
Spivak’s research program on applying category theory as a general theory of agent interactions can be interpeted as a form of categorical pragmatics.
categorical syntax
categorical semantics
Peirce develops a rudimentary speech-act theory within speculative grammar. This is a theory of ‘pragmatics’
sign, object, interpretant
This section will be focused on developing a category theoretic approach to Peirce’s classification of signs, with a particular focus on the speech-act elements of this theory.
This section will re-derive the main results of the 66 classes of signs from the viewpoint of morphisms within category of partial orders.
Another possible structure is the idea of symmetric monoidal categories enriched in posets (i.e. order-enriched), which was discussed by Drew Moshier at the ACT conference.
Intepretation as partial order. Discuss Peirce’s late work three-valued logic. Close relationship between modal ideas and three-valued logic.
Compare to modal intepretation of being-nothing-becoming in Schneider’s work.
deduction, abduction, induction
Peirce’s analysis of the three figures of the syllogism.
Fibrational semantics of the syllogism. General notion of fibration.
alpha, beta, gamma
Existential graphs. State of modal graphs. Categorical interpretation of beta existential graphs. Meilles work on Peirce-like beta graphs.